poisson_probability

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description must fully disclose behavior. It mentions the return type ('Dictionary with probability value and distribution info') and the three probability types, but does not define what each type computes (e.g., point = P(X=k), cumulative = P(X≤k), survival = P(X>k)). It also does not mention edge cases or input constraints, which limits transparency.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is compact and well-organized with an Args/Returns format. Every sentence adds value—parameters are defined precisely, and the return type is stated. There is no fluff or redundancy.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a simple calculator tool with no output schema, the description is largely complete. It covers all parameters, return type, and available probabilistic forms. However, it does not explicitly define the meaning of each prob_type, and does not mention that lam must be positive or that k is a non-negative integer. These are minor gaps, but given the tool's simplicity, the description is nearly sufficient.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The schema has no descriptions for its properties, so the description entirely compensates. It explicitly explains all three parameters: lam ('rate parameter, average events per interval'), k ('Number of events'), and prob_type ('Type of probability ("point", "cumulative", "survival")'). This adds significant meaning beyond the bare schema and is exceptionally clear.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly identifies the tool's function: 'Calculate Poisson probability with different types.' It uses a specific verb and resource, making it clear this handles Poisson distribution calculations. However, it does not explicitly distinguish itself from sibling tools like binomial_probability or normal_probability, so it loses a point for lack of differentiation.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description implies usage through the tool's name and parameter details (e.g., 'average events per interval') but does not explicitly state when to use this tool over alternatives. There is no mention of exclusions or alternative tools, so the guidance is only implicit.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.